# Cross figure

Updated on

A cross-figure (also variously called cross number puzzle or figure logic) is a puzzle similar to a crossword in structure, but with entries which consist of numbers rather than words, with individual digits being entered in the blank cells. The numbers can be clued in various ways:

• The clue can make it possible to find the number required directly, by using general knowledge (e.g. "Date of the Battle of Hastings") or arithmetic (e.g. "27 times 79") or other mathematical facts (e.g. "Seventh prime number")
• The clue may require arithmetic to be applied to another answer or answers (e.g. "25 across times 3" or "9 down minus 3 across")
• The clue may indicate possible answers but make it impossible to give the correct one without using crosslights (e.g. "A prime number")
• One answer may be related to another in a non-determinate way (e.g. "A multiple of 24 down" or "5 across with its digits rearranged")
• Some entries may either not be clued at all, or refer to another clue (e.g. 7 down may be clued as "See 13 down" if 13 down reads "7 down plus 5")
• Entries may be grouped together for clueing purposes, e.g. "1 across, 12 across and 17 across together contain all the digits except 0"
• Some cross-figures use an algebraic type of clue, with various letters taking unknown values (e.g. "A - 2B, where neither A nor B is known in advance)
• Another special type of puzzle uses a real-world situation such as a family outing and base most clues on this (e.g. "Time taken to travel from Ayville to Beetown")

A curious feature of cross-figures is that it makes perfect sense for the setter of a puzzle to try to solve it him or herself. Indeed, the setter should ideally do this (without direct reference to the answer) as it is essentially the only way to find out if the puzzle has a single unique solution. Alternatively, there are computer programs available that can be used for this purpose; however, they may not make it clear how difficult the puzzle is.

Given that some basic mathematical knowledge is needed to solve cross-figures, they are much less popular than crosswords. As a result, very few books of them have ever been published. Dell Magazines publishes a magazine called Math Puzzles and Logic Problems six times a year which generally contains as many as a dozen of these puzzles, which they name "Figure Logics". A magazine called Figure it Out, which was dedicated to number puzzles, included some, but it was very short-lived. This also explains why cross-figures have fewer established conventions than crosswords (especially cryptic crosswords). One exception is the use of the semicolon (;) to attach two strings of numbers together, for example 1234;5678 becomes 12345678. Some cross-figures voluntarily ignore this option and other "non-mathematical" approaches (e.g. palindromic numbers and repunits) where same result can be achieved through algebraic means.

## References

Cross-figure Wikipedia

Topics